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In this work we present different infinite dimensional algebras which appear as deformations of the asymptotic symmetry of the three-dimensional Chern-Simons gravity for the Maxwell algebra. We study rigidity and stability of the infinite dimensional enhancement of the Maxwell algebra. In particular, we show that three copies of the Witt algebra and the $\mathfrak{bms}_{3}\oplus\mathfrak{witt}$ algebra are obtained by deforming its ideal part. New family of infinite dimensional algebras are obtained by considering deformations of the other commutators which we have denoted as $M(a,b;c,d)$ and $\bar{M}(\bar{\alpha},\bar{\beta};\bar{\nu})$. Interestingly, for the specific values $a=c=d=0, b=-\frac{1}{2}$ the obtained algebra $M(0,-\frac{1}{2};0,0)$ corresponds to the twisted Schr\"{o}dinger-Virasoro algebra. The central extensions of our results are also explored. The physical implications and relevance of the deformed algebras introduced here are discussed along the work.
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